After I sent email to conservationists interested in H5N1, suggesting the virus apparently now scarcer in wild birds in Europe, as if self-limiting there too, seen this reply from an ornithologist working on H5N1:

My view of European (and Middle East and now Kazakhstan) outbreaks in wild birds is
(a) the spread did not follow a migration route,
(b) it did not occur at migration time,
(c) the ring recovery on Ruegen island indicated that the whooper swan contracted the virus on Ruegen: this indicates that the virus had been brought there, most likely (in the absecne of poultry infections) through leap-frog infections of birds that died after passing the infection to others,
(d) the movement of birds seems to have been stimulated by adverse weather, driving birds out of the Black Sea area where widespread and persistent infections in poultry had been present all winter.
This argument suggests that the virus remains lethal, and that infected
birds can’t carry it vary far.